Other notable play-off round clashes include Portugal giants Porto drawn against AS Roma, while Spanish club Villarreal will be up against Monaco.
The play-offs are contested over two legs on August 16-17 and 23-24, with the winners going onto the Champions League group phase, reports Efe.
The full draw:
Steaua Bucharest (Romania) vs Manchester City (England)
Porto (Portugal) vs Rome (Italy)
Ajax Amsterdam (Netherlands) vs Rostov (Russia)
BSC Young Boys (Switzerland) vs Borussia Munchengladbach (Germany)
Villarreal (Spain) vs Monaco (France)
Ludogorets (Bulgaria) vs Viktoria Plizen (Czech Republic)
Celtic Glasgow (Scotland) vs Hapoel Beer-Sheva (Israel)
Copenhagen (Denmark) vs Apoel (Cyprus)
Dundalk (Republic of Ireland) vs Legia Warsaw (Poland)
Dinamo Zagreb (Croatia) vs Salzburg (Austria).
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